1. Field of the Invention
The present invention relates to determining the carbon concentration in a silicon single crystal by the Fourier transform infrared spectroscopy (FT-IR). It relates more particularly to a method and an apparatus of determining the substitutional carbon concentration in a silicon single crystal by the FT-IR using a reference of a silicon single crystal.
2. Description of the Related Art
Carbon and oxygen in a silicon single crystal wafer are important factors determining the quality of the wafer. FT-IR is widely employed for determining the carbon concentration in the wafer.
FIG. 9 illustrates an FT-IR optical system. The system comprises a source 1 of infrared light, an aperture device 2, a collimator 3 in the form of concave mirror, a Mickelson interferometer 4, a concave or converging mirror 8, an aperture device 10 and a sensor 11.
The aperture device 2 allows a divergent light from the source 1 of infrared light to pass. The collimator 3 receives the divergent light passing through the aperture device 2 and reflects a beam of collimated infrared light to the Mickelson interferometer 4.
The Mickelson interferometer 4 comprises a beam splitter 5, a fixed mirror 6 and a movable mirror 7. The beam splitter 5 receives the collimated beam from the collimator 3 and splits it into a beam of reflected infrared light and a beam of transmitted infrared light. The fixed mirror 6 reflects the beam of reflected infrared light from the beam splitter 5 back to the beam splitter 5. The movable mirror 7 reflects the beam of transmitted infrared light from the beam splitter 5 back to the beam splitter 5. The beam of reflected infrared light from the fixed mirror 6 and the beam of reflected infrared light from the movable mirror 7 meet at the beam splitter 5 and interfere with each other.
The converging mirror 8 receives the two interfering beams from the Mickelson interferometer 4 and transmits it to a sample 9 to be determined. The sensor 11 receives a light transmitting through the sample 9 and the aperture device 10. An analog/digital convertor (not shown) converts an interferogram output by the sensor 11 into a digital form which is then Fourier-transformed. Thus, an FT-IR concentration determination apparatus detects the infrared absorbance spectrum of the sample 9 and also the infrared absorbance spectrum of a reference in the same manner. FIG. 10 shows the infrared absorbance spectrum of a sample (p-type, 10 .OMEGA.cm) of a silicon single crystal produced by the Czochralski method (referred to as CZ-method produced silicon single crystal hereinafter). FIG. 11 shows the infrared absorbance spectrum of a reference (p-type, 2000 .OMEGA.cm) of a silicon single crystal produced by the floating zone method (referred to as FZ-method produced silicon single crystal hereinafter).
Usually, the FT-IR concentration determination apparatus previously detects the infrared absorbance spectrum of the reference and stores data thereof.
After producing the data of the infrared absorbance spectra of both the sample and the reference regarding the substitutional carbon Cs in a silicon crystal wafer, the FT-IR concentration determination apparatus computes a subtraction factor f for computing a subtraction spectrum between the infrared absorbance spectra of the sample and the reference. Subtracting a product of the subtraction factor and the infrared absorbance spectrum of the reference from the infrared absorbance spectrum of the sample provides the subtraction spectrum between the infrared absorbance spectra of the sample and the reference. FIG. 12 shows the subtraction spectrum between the infrared absorbance spectra of the sample and the reference of FIGS. 10 and 11.
Then, the FT-IR concentration determination apparatus determines the substitutional carbon concentration in the silicon single crystal wafer from the distance (i.e. the height) of the absorption peak of the localized vibration of the substitutional carbon appearing at 605 cm.sup.-1 from a base line, for example, between 595 cm.sup.-1 and 615 cm.sup.-1. A determination of the substitutional carbon concentration provides 0.5 ppma from subtraction spectra of FIG. 12. The lower detective limit of the substitutional carbon concentration is on the order of 0.05 ppma according to the ASTM designation: F123-81.
The process for producing a silicon single crystal substrate for semiconductor devices is categorized into the Czochralski method and the floating zone method. The Czochralski method comprises the steps of placing a raw polysilicon in a quartz crucible, melting the raw polysilicon by a carbon heater, immersing a seed crystal of silicon single crystal in the surface of the melt, and lifting the seed crystal while rotating it to grow a silicon single crystal. The floating zone method comprises the steps of melting part of a raw polysilicon rod by a melting coil to produce a melting zone and moving the melting zone to grow a silicon single crystal.
In comparison, the CZ-method produced silicon single crystal contains more amounts of carbon and oxygen than the FZ-method produced silicon single crystal. It is assumed that carbon invades the CZ-method produced silicon single crystal from the carbon heater, etc. and oxygen invades the CZ-method produced silicon single crystal from the crucible. On the other hand, the FZ-method produced silicon single crystal is substantially carbon-free and oxygen-free. Thus, it has been considered that the FZ-method produced silicon single crystal is more appropriate to the reference for determining the carbon concentration and the oxygen concentration in the CZ-method produced silicon single crystal.
However, the present inventors researched and discovered that an employment of the FZ-method produced silicon single crystal as the reference had problems described below.
As shown in FIG. 13, the absorption peaks of the localized vibration of the substitutional carbon in silicon single crystals appear at 605 cm.sup.-1 and overlap the intense absorption peaks of the silicon phonon. In addition, the forms of the absorption peaks of silicon phonon depend on degrees of free carrier absorption of a dopant and are difference when silicon single crystal wafers have resistivities of 3 .OMEGA.cm and 20 .OMEGA.cm.
Thus, the other effects on differences absorbance between the sample and the reference except the localized vibration peaks of the substitutional carbon and, particularly, the effect of the absorption by the intense silicon phonon and free carriers must be as reduced as possible so that the FT-IR concentration determination apparatus can exactly extract the absorption peak of the localized vibration of the substitutional carbon as the substraction spectrum between the sample and the reference. Therefore, a reference having essentially the same degree of absorption by the silicon phonon and essentially the same degree of free carrier absorption of a dopant which overlap the absorption peak of the localized vibration of the substitutional carbon as a sample must be employed.
However, since the resistivity of the sample of the CZ-method produced silicon single crystal is 20 .OMEGA.cm or less in almost all cases and the resistivity of the reference of the FZ-method produced silicon single crystal, which is normally produced without a dopant, is 1000 .OMEGA.cm or more, the degrees of free carrier absorption of the dopant in the sample and in the reference differ by a large amount.
In addition, the dopant concentration and the oxygen concentration in the FZ-methodical silicon single crystal are much smaller than those in the CZ-method produced silicon single crystal. Thus, the degrees of free carrier absorption of the dopant and the forms of the absorption peak curves by the silicon phonon of the sample and the reference differ greatly from each other. Thus, the absorption peak of the localized vibration of the substitutional carbon is deformed and it is difficult to precisely determine the substitutional carbon concentration of 0.1 ppma or less.
In addition, conventional methods of determining the subtraction factor have a problem in improving the precision. That is, a conventional FT-IR carbon concentration determination apparatus computes the subtraction factor f as a simple ratio of the infrared absorbance (As(.kappa.)) of a sample to the infrared absorbance (Ar(.kappa.)) of a reference at a specified wave number .kappa. by the following equation (1): EQU As(.kappa.)-f.times.Ar(.kappa.)=0 (1),
or as a ratio of an integral of the infrared absorbance (As (.kappa.)) of a sample to an integral of the infrared absorbance (Ar(.kappa.)) of a reference between the limits .kappa.=.kappa.l and .kappa.=.kappa.h in terms of wave number by the following equation (2): ##EQU1##
Since wave number .kappa. is actually determined by a certain resolution, wave numbers are not analog values but discreet values .kappa.n (n=1, 2, 3 . . .). Thus, the equation (2) is actually transformed into the equation (3): ##EQU2##
When computing the subtraction factor by the equation (1), (2) or (3) and the subtraction spectrum using the subtraction factor, the conventional FT-IR carbon concentration determination apparatus cannot suppress aging and the effects of state differences between the sample and the reference (e.g. differences in the thickness and the resistivity) to be least enough so as to be free from the effects of the state differences. Thus, the repeatability of the determination of the same apparatus is poor and errors in the determination between any two conventional FT-IR carbon concentration determination apparatuses of different types are intolerably high.
In wafers of silicon single crystal of today, a required level of the carbon concentration has come down to under 0.05 ppma and the resolution power of the FT-IR carbon concentration determination apparatus has been impressive because of a high quality substrate in use for highly integrated devices and a high-purity device manufacturing process.